Adolf Eichmann on trial in April 1961. He was hanged in 1962 for crimes against humanity. Photograph: Hulton-Deutsch Collection/Corbis

Before the war, Adolf Eichmann, born in 1906, was the acknowledged "Jewish expert" of the SS, in charge of carrying out various schemes to remove the Jews from Germany, such as encouraging – or forcing – them to emigrate, or transporting them to Madagascar. When the Germans invaded first Poland in 1939, then the Soviet Union two years later, Eichmann organised the concentration of the millions of Jews who lived in eastern Europe into ghettos, and then ensured they were taken, along with Jews from every part of Europe under Nazi control or influence, to camps such as Auschwitz, to be murdered. After Germany's defeat, Eichmann went underground and then escaped to Argentina, where he joined a number of other senior Nazis in exile, living under an assumed name. During the 1950s, however, his whereabouts were discovered, and, in 1960, he was kidnapped by Mossad agents and smuggled out to Jerusalem, where he was put on trial for mass murder, found guilty, and, in 1962, hanged.

During his trial, as he sat in the bullet-proof glass box that served as the dock, Eichmann did not give the impression of being a monster, a sadist or a thug. He presented himself, on the contrary, as an ordinary, reasonable man. He was not personally, physically brutal or violent. When he had visited the scenes of extermination, he had clearly felt rather queasy. Yet here was a man who, notoriously, had said towards the end of the war that if Germany lost, he would "leap laughing into the grave because the feeling that he had 5 million enemies of the Reich on his conscience would be for him a source of extraordinary satisfaction".

So what kind of a man was Adolf Eichmann? How and why did he become a mass murderer? The first and still the most famous and influential attempt to answer these questions came from the German-Jewish philosopher Hannah Arendt, who attended the trial as a correspondent for the New Yorker, subsequently publishing her articles in a revised book-length version as Eichmann in Jerusalem. The book stirred up a storm of criticism, particularly though not exclusively from Jewish intellectuals in the United States. There were many reasons for this. Reflecting what was known at the time, and in common with other early historians of the Nazis' genocide of the Jews, Arendt was highly critical both of the passivity of the great majority of European Jews in the face of persecution and extermination, and of the collaborationist administration of the Jewish Councils in the ghettos, whose tragic and impossible situation failed to arouse her sympathy.

The judgments she offers in Eichmann in Jerusalem are utterly independent and totally unsparing. Time and again she raises questions that provoke and disturb. The abduction of Eichmann from Argentina was illegal; the trial was a show-trial; Israel's marriage laws were similar to the racist Nuremberg laws of the Nazis; Eichmann's crimes were crimes against humanity, so international law should have dealt with the case. Arendt's independence of mind is one of the most impressive features of her reporting. She writes as a detached philosophical inquirer, not as the representative of any particular group or political tendency.

Eichmann in Jerusalem bore the subtitle "A Study in the Banality of Evil". What she meant by this was not that Eichmann was a mere bureaucrat, a conscienceless pen-pusher who was only obeying orders. On the contrary, she argued, he was an ideological antisemite, a man of overweening ambition who wanted not only power but also fame. He had a compulsion to "talk big", she observed, and indeed "bragging was the vice that was Eichmann's undoing". Not a particularly intelligent man, he assimilated the ideology and behaviour of the evil system within which he sought to achieve distinction. He admired the Third Reich not least because it allowed men from a humble background like his own – or Hitler's, for that matter – to climb to the top. He was under no compulsion to act as he did: he could have opted out at any time; all his actions were voluntary. He deserved to die because he had failed, or refused, to exercise the kind of moral judgment Arendt herself showed in her book. His crimes were the crimes of a system, even a nation; as the psychologists who examined him in prison concluded, he was not a psychopath or a sociopath, though, as Arendt points out, he was most certainly, and frequently, a liar and a deceiver. This was the "banality of evil".

In Argentina, Arendt notes, Eichmann did not go underground but occupied himself with "talking endlessly with members of the large Nazi colony, to whom he readily admitted his identity". These conversations were recorded by a Dutch ex‑member of the SS, Willem Sassen, and edited extracts were published anonymously, though there could be little doubt about the identity of the principal participant. The existence of the original tapes and transcripts has long been known, but up to now their poor quality has defied systematic investigation. The German philosopher and historian Bettina Stangneth has now performed the invaluable service of deciphering them, putting them together with other, often little-known source material, and delivering a full analysis of Eichmann's ideas as he expounded them to his friends and former colleagues in exile.

In the conversations he had with Sassen and others, Eichmann was completely unrepentant about the extermination of the Jews, which he saw as historically necessary, a policy he was proud to have carried out in the interests of Germany. The cynicism, inhumanity, lack of pity and moral self‑deception of the conversations are breathtaking. This is a very disturbing book, and every now and then, as you read it, you have to pause in disbelief. Ten years and more after the war's end, Eichmann's lack of realism, typical for a political exile, even persuaded him that he could make a comeback, or that nazism could be rehabilitated, and he planned to launch a public defence of what he saw as its achievements.

In one of the conversations, Eichmann described himself as a "cautious bureaucrat" but also "a fanatical warrior, fighting for the freedom of my blood". Stangneth dissents from Arendt's belief that Eichmann was unintelligent, and points out that he calculatedly presented himself only as the cautious bureaucrat during his trial, deliberately concealing his "fanatical" side. But his clumsy attempt to present himself as pursuing a Kantian "categorical imperative" does not show that he was in any way an intellectual; and his mendacious self-presentation as a mere pen-pusher did not convince anyone, least of all Arendt. What he lacked was moral intelligence, the ability to judge the system he worked for and whose ideology he assimilated so completely.

Stangneth's absorbing account of his years in exile, which is translated by Ruth Martin, adds considerably to our knowledge of Eichmann, but it is not a "total reassessment of the man", as the publishers claim, nor is it true to claim that the book "permanently undermines Hannah Arendt's notion of the 'banality of evil'". Half a century after it was written, Arendt's book, despite the fact that it has been overtaken in many of its details by research, remains a classic that everyone interested in the crimes of nazism has to confront.

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